On the CR transversality of holomorphic maps into hyperquadrics

Let $M_\ell$ be a smooth Levi-nondegenerate hypersurface of signature $\ell$ in $\mathbf C^n$ with $n\ge 3$, and write $H_\ell^N$ for the standard hyperquadric of the same signature in $\mathbf C^N$ with $N-n< \frac{n-1}{2}$. Let $F$ be a holomorphic map sending $M_\ell$ into $H_\ell^N$. Assume $F$ does not send a neighborhood of $M_\ell$ in $\mathbf C^n$ into $H_\ell^N$. We show that $F$ is necessarily CR transversal to $M_\ell$ at any point. Equivalently, we show that $F$ is a local CR embedding from $M_\ell$ into $H_\ell^N$.Comment: To appear in Abel Symposia, dedicated to Professor Yum-Tong Siu on the occasion of his 70th birthda

Formal and finite order equivalences

We show that two families of germs of real-analytic subsets in $C^{n}$ are formally equivalent if and only if they are equivalent of any finite order. We further apply the same technique to obtain analogous statements for equivalences of real-analytic self-maps and vector fields under conjugations. On the other hand, we provide an example of two sets of germs of smooth curves that are equivalent of any finite order but not formally equivalent

Comparing Different Template Features for Recognizing People by Their Gait

To recognize people by their gait from a sequence of images, we have proposed a statistical approach which combined eigenspace transformation (EST) with canonical space transformation (CST) for feature transformation of spatial templates. This approach is used to reduce data dimensionality and to optimize the class separability of different gait sequences simultaneously. Good recognition rates have been achieved. Here, we incorporate temporal information from optical flows into three kinds of temporal templates and use them as features for gait recognition in addition to the spatial templates. The recognition performance for four kinds of template features has been evaluated in this paper. Experimental results show that spatial templates, horizontal-flow templates and the combined horizontal-flow and vertical-flow templates are better than vertical-flow templates for gait recognition

Model of a fluid at small and large length scales and the hydrophobic effect

We present a statistical field theory to describe large length scale effects induced by solutes in a cold and otherwise placid liquid. The theory divides space into a cubic grid of cells. The side length of each cell is of the order of the bulk correlation length of the bulk liquid. Large length scale states of the cells are specified with an Ising variable. Finer length scale effects are described with a Gaussian field, with mean and variance affected by both the large length scale field and by the constraints imposed by solutes. In the absence of solutes and corresponding constraints, integration over the Gaussian field yields an effective lattice gas Hamiltonian for the large length scale field. In the presence of solutes, the integration adds additional terms to this Hamiltonian. We identify these terms analytically. They can provoke large length scale effects, such as the formation of interfaces and depletion layers. We apply our theory to compute the reversible work to form a bubble in liquid water, as a function of the bubble radius. Comparison with molecular simulation results for the same function indicates that the theory is reasonably accurate. Importantly, simulating the large length scale field involves binary arithmetic only. It thus provides a computationally convenient scheme to incorporate explicit solvent dynamics and structure in simulation studies of large molecular assemblies

Asymmetric Reactions of Abnormal Audit Fee Jump to Credit Rating Changes

Abstract Considering the inherent stickiness of abnormal audit fees, our study contributes to the literature by decomposing abnormal audit fees into a jump component and long-run sticky component. We investigate whether and how changes in credit ratings asymmetrically affect the jump component of abnormal audit fees. We document a positive association between rating downgrades and the jump component. We find that heightened bankruptcy risk and misstatement risk are the mechanisms that drive this relationship. Further analysis shows that firms experiencing rating downgrades are more likely to receive a going concern opinion and experience longer audit report lags. Taken together, our findings provide direct evidence that credit ratings are significantly associated with abnormal audit fees, particularly with the jump component. Given the serial correlation of abnormal audit fees, our study sheds light on the importance of disaggregation of the abnormal audit fee residuals into the jump and long-run sticky components

Fuzzy Rings in D6-Branes and Magnetic Field Background

We use the Myers T-dual nonabelin Born-Infeld action to find some new nontrivial solutions for the branes in the background of D6-branes and Melvin magnetic tube field. In the D6-Branes background we can find both of the fuzzy sphere and fuzzy ring solutions, which are formed by the gravitational dielectric effect. We see that the fuzzy ring solution has less energy then that of the fuzzy sphere. Therefore the fuzzy sphere will decay to the fuzzy ring configuration. In the Melvin magnetic tube field background there does not exist fuzzy sphere while the fuzzy ring configuration may be formed by the magnetic dielectric effect. The new solution shows that $D_0$ propagating in the D6-branes and magnetic tube field background may expand into a rotating fuzzy ring. We also use the Dirac-Born-Infeld action to construct the ring configuration from the D-branes.Comment: Latex, 15 pages, detailed comments in section 2, typos correcte

Hermitian symmetric polynomials and CR complexity

Properties of Hermitian forms are used to investigate several natural questions from CR Geometry. To each Hermitian symmetric polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the polynomial product. We show, except for three trivial cases, that every signature pair can be obtained from the product of two indefinite forms. We provide several new applications to the complexity theory of rational mappings between hyperquadrics, including a stability result about the existence of non-trivial rational mappings from a sphere to a hyperquadric with a given signature pair.Comment: 19 pages, latex, fixed typos, to appear in Journal of Geometric Analysi

Controlled Growth, Patterning and Placement of Carbon Nanotube Thin Films

Controlled growth, patterning and placement of carbon nanotube (CNT) thin films for electronic applications are demonstrated. The density of CNT films is controlled by optimizing the feed gas composition as well as the concentration of growth catalyst in a chemical vapor deposition process. Densities of CNTs ranging from 0.02 CNTs/{\mu}m^2 to 1.29 CNTs/{\mu}m^2 are obtained. The resulting pristine CNT thin films are then successfully patterned using either pre-growth or post-growth techniques. By developing a layered photoresist process that is compatible with ferric nitrate catalyst, significant improvements over popular pre-growth patterning methods are obtained. Limitations of traditional post-growth patterning methods are circumvented by selective transfer printing of CNTs with either thermoplastic or metallic stamps. Resulting as-grown patterns of CNT thin films have edge roughness (< 1 {\mu}m) and resolution (< 5 {\mu}m) comparable to standard photolithography. Bottom gate CNT thin film devices are fabricated with field-effect mobilities up to 20 cm^2/Vs and on/off ratios of the order of 10^3. The patterning and transfer printing methods discussed here have a potential to be generalized to include other nanomaterials in new device configurations

Adaptive compliance shaping with human impedance estimation

Robotics has been a promising and popular research area for the past few decades. Among various applications of robotic, in many cases, human are involved in different manners. Therefore, as an important sub research area of robotics, human robot interaction has drawn decent attention recently. It has been deeply and widely studied. For human robot interaction, human play an important role. Undoubtedly, the more we know about human, the easier we can do human robot interaction and the better performance we can achieve in human robot interaction. One fascinating research topic of human robot interaction would be human in exoskeleton, where human play a key role in the mechanical design of exoskeleton as well as the control strategy design of exoskeleton. Among all those applications, the augmentation exoskeleton is especially interesting due to its ability to amplify human. As mentioned previously, human properties are important for the design of exoskeleton. Unfortunately, despite many inspiring and deep studies about human properties and various proposed human models, human remains to be a complicated system that is hard to predict and model. Furthermore, human is a dynamic system whose parameters keep changing with time, bringing more challenges. As we all know, limited understanding of the control plant will limit the performance of the controller and bring difficulties in the design of a controller. In fact, the performance of many existed controller for augmentation exoskeleton is limited by using conservative values of human property parameters. A straightforward way to solve this problem is to estimate human properties online. Under this circumstance, the main challenges are to develop a control strategy, whose performance can be exploited using the estimation of human properties and a reliable method to online estimate human properties. This thesis mainly presents an adaptive compliance shaping control strategy with human impedance estimation and a brief review of a newly proposed complex stiffness model of human.Mechanical Engineerin

Twist-3 Distribute Amplitude of the Pion in QCD Sum Rules

We apply the background field method to calculate the moments of the pion two-particles twist-3 distribution amplitude (DA) $\phi_p(\xi)$ in QCD sum rules. In this paper,we do not use the equation of motion for the quarks inside the pion since they are not on shell and introduce a new parameter $m_0^p$ to be determined. We get the parameter $m_0^p\approx1.30GeV$ in this approach. If assuming the expansion of $\phi_p(\xi)$ in the series in Gegenbauer polynomials $C_n^{1/2}(\xi)$, one can obtain its approximate expression which can be determined by its first few moments.Comment: 12 pages, 3 figure